Medical errors are common in hospitals throughout the world. One possible causal factor is the long work hours of hospital personel. In a pilot study investigating this issue, medical residents were encouraged to sleep 6-8 hours per night for a 3-week period instead of thier usual irregular sleep schedule. The researchers expected, given previous data, that there would be one medical error per resident per day on thier usual irregular sleep schedule.
Suppose two residents participate in the program (each for 3 weeks), and chart review finds a total of 20 medical errors made by the two residents combined.
What test can be used to test the hypothesis that an increase in amount of sleep will change the number of medical errors per day?
Implement the test in above Problem, and report a two-tailed P-value.
What would be the power of the type of test used in Problem above under these assumptions? (Hint: Use the normal approximation to the Poisson distribution.